Abstract
The finite horizon H 2/H ∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, the authors derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linearquadratic (LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H 2/H ∞ control of meanfield type via the solvability of coupled matrix-valued equations.
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This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61573227, 61633014, the Research Fund for the Taishan Scholar Project of Shandong Province of China, the SDUST Research Fund under Grant No. 2015TDJH105, and the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources under Grant No. LAPS16011
This paper was recommended for publication by Editor CHEN Jie
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Zhang, W., Ma, L. & Zhang, T. Discrete-time mean-field stochastic H 2/H ∞ control. J Syst Sci Complex 30, 765–781 (2017). https://doi.org/10.1007/s11424-017-5010-6
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DOI: https://doi.org/10.1007/s11424-017-5010-6